TY - JOUR
T1 - Construction of L2-orthogonal elements of arbitrary order for Local Projection Stabilization
AU - Schieweck, F.
AU - Skrzypacz, P.
AU - Tobiska, L.
N1 - Funding Information:
The presented work in this paper was supported through the research grant 090118FD5347 from the Nazarbayev University.
Publisher Copyright:
© 2018 Elsevier Inc.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/11/15
Y1 - 2018/11/15
N2 - We construct L2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.
AB - We construct L2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.
KW - L-orthogonal elements
KW - Local projection stabilization
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U2 - 10.1016/j.amc.2018.04.070
DO - 10.1016/j.amc.2018.04.070
M3 - Article
AN - SCOPUS:85047777366
VL - 337
SP - 87
EP - 101
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -